3y(4y-35)=180

Solution for 3y(4y-35)=180 equation:

Simplifying
3y(4y + -35) = 180

Reorder the terms:
3y(-35 + 4y) = 180
(-35 * 3y + 4y * 3y) = 180
(-105y + 12y2) = 180

Solving
-105y + 12y2 = 180

Solving for variable 'y'.

Reorder the terms:
-180 + -105y + 12y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -105y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -35y + 4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-60 + -35y + 4y2)' equal to zero and attempt to solve:

Simplifying
-60 + -35y + 4y2 = 0

Solving
-60 + -35y + 4y2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-15 + -8.75y + y2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8.75y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + -8.75y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8.75y + y2 = 0 + 15
-8.75y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8.75y + y2 = 15

The y term is -8.75y.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75y + 19.140625 + y2 = 15 + 19.140625

Reorder the terms:
19.140625 + -8.75y + y2 = 15 + 19.140625

Combine like terms: 15 + 19.140625 = 34.140625
19.140625 + -8.75y + y2 = 34.140625

Factor a perfect square on the left side:
(y + -4.375)(y + -4.375) = 34.140625

Calculate the square root of the right side: 5.842997946

Break this problem into two subproblems by setting 
(y + -4.375) equal to 5.842997946 and -5.842997946.

Subproblem 1
y + -4.375 = 5.842997946

Simplifying
y + -4.375 = 5.842997946

Reorder the terms:
-4.375 + y = 5.842997946

Solving
-4.375 + y = 5.842997946

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '4.375' to each side of the equation.
-4.375 + 4.375 + y = 5.842997946 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + y = 5.842997946 + 4.375
y = 5.842997946 + 4.375

Combine like terms: 5.842997946 + 4.375 = 10.217997946
y = 10.217997946

Simplifying
y = 10.217997946

Subproblem 2
y + -4.375 = -5.842997946

Simplifying
y + -4.375 = -5.842997946

Reorder the terms:
-4.375 + y = -5.842997946

Solving
-4.375 + y = -5.842997946

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '4.375' to each side of the equation.
-4.375 + 4.375 + y = -5.842997946 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + y = -5.842997946 + 4.375
y = -5.842997946 + 4.375

Combine like terms: -5.842997946 + 4.375 = -1.467997946
y = -1.467997946

Simplifying
y = -1.467997946

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.217997946, -1.467997946}
Solution
y = {10.217997946, -1.467997946}